Generators of simple Lie algebras in arbitrary characteristics
Representation Theory
2008-07-14 v2 Algebraic Geometry
Rings and Algebras
Abstract
In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.
Keywords
Cite
@article{arxiv.0708.1711,
title = {Generators of simple Lie algebras in arbitrary characteristics},
author = {Jean-Marie Bois},
journal= {arXiv preprint arXiv:0708.1711},
year = {2008}
}
Comments
26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.3